Sufficient Conditions for Subordination of Meromorphic Functions

Problem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various researchers. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, by having new operators, new criteria and new set of subordination theorems could be obtained with some earlier results and standard methods.